Albedo and size determination of potentially hazardous asteroids: (99942) Apophis

Icarus 188 (2007) 266–269 www.elsevier.com/locate/icarus

Note

Albedo and size determination of potentially hazardous asteroids: (99942) Apophis ✩ M. Delbò a,b,∗ , A. Cellino b , E.F. Tedesco c a Laboratoire Cassiopée, Observatoire de la Côte d’Azur, BP 4229, 06304 Nice Cedex 04, France b INAF, Osservatorio Astronomico di Torino, Pino Torinese, Italy c Space Science Center, University of New Hampshire, Durham, NH 03824, USA

Received 15 June 2006; revised 5 December 2006 Available online 30 January 2007

Abstract The near-Earth object (99942) Apophis will make an extremely close approach to the Earth in 2029, and currently has approximately a one-in-45,000 chance of impacting our planet in 2036 (JPL Sentry, November 2006). Computation of the orbital evolution of this object is limited by insufficient knowledge of physical properties required to determine the role played by non-gravitational effects. Using polarimetric observations, we have obtained the first reliable determination of the albedo of Apophis, obtaining 0.33 ± 0.08. We also derive an updated estimate of the asteroid’s absolute magnitude: H = 19.7 ± 0.4. Using this albedo and H , we find that Apophis has a diameter of 270 ± 60 m, slightly smaller than preliminary estimates based upon an assumed albedo. Our observations demonstrate the feasibility of polarimetric observations aimed at obtaining albedos and sizes of small, potentially hazardous asteroids. © 2007 Elsevier Inc. All rights reserved. Keywords: Asteroids; Near-Earth objects; Polarimetry; Photometry

1. Introduction The near-Earth object (NEO) (99942) Apophis (principal provisional designation 2004 MN4 ) was discovered on June 19, 2004, and recovered on December 19, 2004. A few days later, both Sentry and NEODys (Milani et al., 2005), the automated collision monitoring systems operated at the NASA-JPL and at the University of Pisa (Italy) and Valladolid (Spain), reported a threat of impact with the Earth on April 13, 2029. The impact probability originally computed was 1/300, and Apophis was the first asteroid to reach a rank higher than 1 in the Torino scale, which is used to describe the hazard posed by near-Earth objects based on their impact probability and delivered impact energy in the case of a collision with our planet (Binzel, 2000). Over the next few days, on the basis of further astrometric observations posted to NASA’s Sentry and NEODys, the impact probability continued to increase reaching a peak of 2.7% on December 27, 2004, when pre-discovery observations of March 2004 ruled out any possibility of impact in 2029. However, current predictions (Chesley, 2005, 2006), including radar observations, indicate that in April 2029 Apophis will experience a very close approach with the Earth, with a minimum distance from the geocenter of 5.98±0.26R⊕ at 3σ (R⊕ = 6378 km is the Earth radius). Such a close encounter with the Earth will strongly modify the post-2029 orbit of Apophis, leading to a number of possible resonant returns (see Chesley, 2005; ✩

Based on observations performed at the European Southern Observatory (ESO) DDT request 276.C-5030. * Corresponding author. Fax: +33 (0) 4 9200 3121. E-mail address: [email protected] (M. Delbò). 0019-1035/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2006.12.024

Milani et al., 1999) between the years 2036–2054 (April 13, 2036 being the most likely), keeping the asteroid at level 1 on the Torino impact hazard scale. As of November 2006, the cumulative impact probability is 1 in 45,000 (http://neo.jpl.nasa.gov/risk/a99942.html), or 1 in 48,000 (http://newton.dm. unipi.it/cgi-bin/neodys/neoibo?riskpage:0;main). Due to its peculiar orbital properties, which could eventually lead Apophis to collide with the Earth, it is obviously of the highest interest to obtain information on the physical properties of this object. In particular, it is extremely important to assess its size, since in the case of a collision the impact energy is proportional to the third power of the impactor’s size. Apophis is too small to allow a size measurement based on direct optical imaging and it does not approach the Earth closely enough before 2029 for a radar size to be obtained. Therefore, we must rely on indirect techniques. Current diameter estimates, which range from 320 to 970 m (http://neo.jpl.nasa.gov/risk/a99942.html, http://earn.dlr.de/nea/099942.htm), are based on an assumed albedo. In this paper we present a new, refined estimate of Apophis’ size, based on the first determination of its albedo, by means of polarimetric observations, coupled with an improved determination of its absolute magnitude. 2. Asteroid polarimetry Polarimetry has long been recognized as one of the best techniques to derive asteroid albedos. The light that we receive from these bodies at visible wavelengths consists of sunlight scattered by their solid surfaces. As a consequence, the visible light from these objects is in a state of partial linear polarization, which varies for different illumination conditions, described by the phase angle

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Table 1 Observing log and results of VLT observations of Apophis. We give the epoch in Julian Day and date UT Date UT

Photometry (mag)

Polarimetry

yy

mn Day hh min sec

mV

P (%) σP

Run A 2453782.752786 2453782.757287 2453782.760501 2453782.770194 2453782.782342

2006 2006 2006 2006 2006

02 02 02 02 02

16 16 16 16 16

06 06 06 06 06

04 10 15 29 46

00.710 29.597 07.286 04.762 34.349

19.49 21.51 19.53 21.55 19.54 21.56

0.04 0.04 0.04

19.61 21.63

0.03

Run B 2453801.861058 2453801.872158 2453801.881571 2453801.894298

2006 2006 2006 2006

03 03 03 03

07 07 07 07

08 08 09 09

39 55 09 27

55.411 18.83 21.44 54.451 18.87 21.48 27.734 47.347 18.96 21.57

0.02 0.02

Run C 2453822.821170 2453822.822445 2453822.826146 2453822.842105 2453822.856533

2006 2006 2006 2006 2006

03 03 03 03 03

28 28 28 28 28

07 07 07 08 08

42 44 49 12 33

29.088 19.248 39.014 37.872 24.451

19.31 22.58 19.25 22.53 19.31 22.58

0.03 0.03 0.03

19.31 22.58

0.03

Run D 2453827.837966 2453827.839237 2453827.842729 2453827.855385 2453827.870070 2453827.871445

2006 2006 2006 2006 2006 2006

04 04 04 04 04 04

02 02 02 02 02 02

08 08 08 08 08 08

06 08 13 31 52 54

40.262 30.077 31.786 45.264 54.048 52.848

19.01 22.41 19.11 22.50 19.00 22.40

0.01 0.01 0.01

19.24 22.63 19.22 22.61

0.01 0.01

JD

V (αi ) σmV

3.28

3.70

Ephemerides PA (◦ ) σPA

0.36 20.6

0.12 10.7

3.1

0.9

Pr (%) σPr

3.25

3.70

0.02

4.40

4.65

0.11 −0.6

0.07 −6.2

0.7

0.4

4.37

4.65

r (AU)  (AU) α (◦ )

1.0890 1.0890 1.0890 0.41 1.0890 1.0890

0.3622 0.3622 0.3622 0.3622 0.3621

64.4 64.4 64.4 64.4 64.4

1.0628 1.0628 0.13 1.0628 1.0627

0.2828 0.2828 0.2828 0.2827

68.1 68.1 68.1 68.1

1.0162 1.0162 1.0162 0.12 1.0161 1.0161

0.2179 0.2179 0.2179 0.2179 0.2179

79.1 79.1 79.1 79.1 79.1

1.0026 1.0026 1.0025 0.07 1.0025 1.0025 1.0025

0.2091 0.2091 0.2091 0.2090 0.2090 0.2090

83.2 83.2 83.2 83.2 83.2 83.2

mV is the measured magnitude in the V -band, σmV its uncertainty and V (αi ) is V reduced to 1 AU heliocentric and geocentric distances. P is the measured degree of linear polarization, σP its uncertainty; PA is the position angle (with respect to the North) of the polarization plane and σPA its uncertainty. Pr is equal to P cos(2θ), where θ is the angle between the plane of polarization and the plane normal to the scattering plane (the Earth–Sun–asteroid plane). r is the heliocentric,  the geocentric distance and α the phase angle. All observations were carried out in the V -band (V Bessel filter). (the angle between the directions of the Earth and the Sun as seen from the asI −I

teroid). Variations of the parameter Pr = I⊥ +I|| as a function of phase angle ⊥ || have been used to describe the polarimetric behavior of asteroids (Dollfus and Zellner, 1979; Dollfus et al., 1989; Cellino et al., 1999, 2005). In the above definition I⊥ and I|| indicate the intensity of the incoming light having the plane of polarization perpendicular and parallel to the scattering plane, respectively (the scattering plane being the plane containing the asteroid, the Sun and the Earth at the epoch of observation). When one plots the variation of Pr as a function of the phase angle, a well defined curve is obtained (see, e.g., Dollfus and Zellner, 1979; Dollfus et al., 1989). The typical behavior consists of the presence of a range of phase angles, approximately between 0◦ and 20◦ , for which Pr is negative reaching a minimum at phase angles around 10◦ . This general behavior characterizes, with some minor differences depending on the taxonomic class, all asteroids observed so far. Beyond a phase angle of about 20◦ , the polarization usually changes sign. Around and beyond the inversion angle, the trend of Pr for increasing phase angle is essentially linear, and a well defined relation is known to exist between the slope h of the polarization curve and the albedo pV of the surfaces, the so-called slope-albedo relation, which takes the form: log(pV ) = c1 log(h) + c2 . The most recent derivation of the c1 and c2 coefficients has been published by Cellino et al. (1999). 3. Apophis observations, data reduction and results Due to the faintness of this small asteroid (V ∼ 19.5), the observations were carried out using FORS1 (Appenzeller et al., 1998) at the 8.2 m VLT-Kueyen telescope of the European Southern Observatory. In particular, we measured the degree of linear polarization of Apophis on four nights in February through April 2006. Our polarization measurements were obtained at phase angles between 64.4◦ and 83.2◦ . We used standard procedures (see, e.g., Fornasier et al., 2006) for data acquisition, calibration and reduction. Linear polarization measurements were obtained in the V -band at 4 angles of the λ/2 retarder plate (0◦ , 22.5◦ , 45◦ and 67.5◦ ), and were bracketed by V -band photometry. This

Fig. 1. Polarization-phase curve for Apophis from our measurements: The plot shows also the obtained linear fit of the data. The corresponding value of the linear slope is given. The linear slope, h, is function of the geometric visible albedo of the asteroid pV via the relation: log(pV ) = −1.118 log(h) − 1.799 (see Cellino et al., 1999). was done to obtain V magnitude measurements, useful to determine the absolute magnitude, and also to monitor possible lightcurve variations during the polarization measurements, which, as expected given Apophis’ 1.27 day rotation period (Behrend, R., 2004. http://obswww.unige.ch/~behrend/page5cou. html#099942), were found to be negligible. Our results are given in Table 1 and the resulting polarization-phase curve is shown in Fig. 1. We note that the phase angle of intercept of the linear fit to our polarimetric data is consistent

268

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with the intercept angle of ∼20◦ observed for most asteroids. This gives high confidence that the fitted linear slope is not very different from what would be observed at lower phase angle. Using the most recent calibration of the polarimetric slope–albedo relation (Cellino et al., 1999), from the data shown in Table 1 we derived a corresponding albedo of 0.33 ± 0.08. The above albedo uncertainty is obtained by means of a formal propagation of the errors, including not only the nominal errors in the determination of the degree of linear polarization and the position angle of the polarization plane, determined by data reduction, but also the nominal uncertainties of the two coefficients c1 and c2 of the polarimetric slope–albedo relation (see above). Our resulting albedo is consistent with the Q-like spectrum observed for Apophis (Binzel et al., 2006) and with the mean geometric visible albedo, pV  = 0.35, for the 4 NEAs of this type for which we have radiometric data (Delbò, 2004). We note that the uncertainty in the albedo is mainly due to the uncertainties in the coefficients of the slope–albedo law, and not by the uncertainty in the slope derived from our observations. The albedo uncertainty varies directly proportional to the uncertainties in the slope–albedo law coefficients. This fact highlights the need to produce a new, more accurate, calibration of the slope–albedo law, work on which is currently underway. This new calibration, based on a homogeneous set of observations of asteroids with well-determined albedos, e.g., those from Shevchenko and Tedesco (2006), will result in a significant improvement of the polarimetric method for deriving asteroid albedos. However, even the current slope–albedo law yields albedos with uncertainties up to a factor of three lower than those obtained using single-waveband radiometric observations. We used default values for the V -band photometric zero point (28.111 mag) and extinction coefficient (0.12 mag/airmass) at Cerro Paranal to calibrate the photometric observations. By comparing our magnitudes, reduced to 1 AU heliocentric and geocentric distances—V (αi ) (Bowell et al., 1989), where the index i ranges over the set of observations of Table 1—to a lightcurve of Apophis obtained at similar phase and aspect angles (Behrend, R., 2004. http://obswww.unige.ch/~behrend/page5cou.html#099942), we found that the polarimetric observations of our runs A and B should have been obtained near lightcurve maximum, whereas those of runs C and D were near lightcurve minimum. We then extrapolated each V (αi ) magnitude to α = 0◦ , using the standard (H , G) system (Bowell et al., 1989) to describe the variation of magnitude as a function of phase angle. In doing so, we assumed a slope parameter G = 0.25 for the magnitude–phase relation—the most common value for S- and Q-class asteroids (Bowell et al., 1989), and we derived the corresponding best-fit value for the absolute magnitude H of Apophis. We did not try to derive simultaneously both the H and G parameters from our observations, because they are a very limited sample, covering a range of quite large phase angles, well beyond the limits that are reached in observations of main-belt asteroids. Under these conditions a reliable (H , G) fit cannot be obtained. By assuming a priori G = 0.25, we obtain H = 19.7 ± 0.3 mag, where the uncertainty is the standard deviation of the extrapolated V (αi ) values. Note that the error indicated here is only the nominal value computed in our best-fit, and is certainly underestimated, for the reasons explained below. For example, using the default value G = 0.15, which is commonly adopted when no other information is available for a given object, would correspondingly yield an absolute magnitude slightly brighter, namely H = 19.5 ± 0.3 mag. Using the albedo derived from the polarimetric observations, and the H value from our V -band photometry, the diameter D (in km) of Apophis can be found from: −1/2

D = 1329pV

× 10−H /5 .

The diameter value derived from the above formula has an associated uncertainty that can be computed by means of a formal propagation of the errors in albedo and absolute magnitude. In the present case, the major source of uncertainty comes from the large error bar of H . As we have seen above, the accuracy of our derived H value is strongly affected by the poor knowledge of the slope parameter (G). In order to show how the computation of the size and its associated uncertainty depend on the adopted H value and its uncertainty, in Table 2 we list three possible options. The first option assumes the H = 19.2 value currently listed (as of November 2006) by the MPC. We find that in this case the H uncertainty is about 0.5 mag. The reason is that a number of different authors has recently pointed out the existence of significant errors

Table 2 Resulting diameter and corresponding uncertainty of 99942 Apophis, for different possible choices of the absolute magnitude H , computed by taking into account H uncertainties and using our derived albedo value of 0.33 ± 0.08 H

σH

G

D (m)

σD (m)

19.2(a)

0.5 0.4 0.4

NA 0.15 0.25

335 290 266

87 64 58

19.5(b) 19.7(c)

Case (a): H taken from the MPC (November 2006); (b) H derived from a fit of our data using a default G value of 0.15; (c) the same as (b) but using the G = 0.25 value, appropriate for S type asteroids. in the H values listed by the MPC, with a possible systematic underestimate of H on the order of 0.5 mag for objects as faint as Apophis (Juri´c et al., 2002; Tedesco et al., 2005). The diameter derived assuming the above H value and an albedo of 0.33 ± 0.08 determined from polarimetry, is 335 ± 90 m. The second option is to use the H value derived from our photometric observations, assuming the default value G = 0.15. In this case, assuming an uncertainty of the order of 0.15 for G, we estimate that the final uncertainty in H cannot be much better than 0.4 mag. The resulting diameter in this case is 290 ± 60 m. The third option listed in Table 2 is similar, but uses an assumed G value of 0.25 to derive H . Since we know that this is the value of G that applies to objects of the same taxonomic class as Apophis, this is our preferred option, since it uses all the limited information available for this object. The corresponding diameter in this case is 270 ± 60 m. Apart from the case of the option based on the MPC H value, the diameter values shown in Table 2 are mutually consistent within the error bars, and are rather smaller than previous estimates (see http://neo.jpl.nasa.gov/risk/a99942. html, http://earn.dlr.de/nea/099942.htm). We note also that the relative uncertainty in the diameter is on the order of 20%, a fairly reasonable result. 4. Discussion We stress that after our polarimetric observations the largest source of uncertainty in the size of Apophis comes from the large uncertainty in H . If this parameter significantly differs from those considered here and shown in Table 2, due, e.g., to a non-standard visual phase function, something we cannot exclude a priori, the size will change correspondingly, even beyond the nominal uncertainty given above. It is clear, then, that accurate magnitude measurements at moderate values of the phase angle in the future will greatly reduce the size uncertainty. For the purposes of future observations, we note that Apophis will reach a phase angle of ∼32◦ in January 2013, ∼21◦ in late February 2021, and will be at phase angles between 4.5◦ and 20◦ between 13 November and 15 December 2029. The impact of an asteroid with a diameter of 250 m is expected to deliver an energy of 400 Mt for an impact velocity of 12.6 km/s and an assumed bulk density of 2.6 g/m3 (see http://neo.jpl.nasa.gov/risk/a99942.html). Note that the impact velocity of Apophis is much smaller than the average impact velocity of NEAs. Scaling the impact energy to a diameter of 270 m, a rounded-number energy would be ∼500 Mt, and for a diameter of 290 m, ∼700 Mt. These observations show how reliable albedos and (assuming reliable H values can be obtained) sizes can be obtained by means of polarimetric observations for faint (V > 20) asteroids. Such data are difficult to obtain with other techniques, such as thermal infrared observations, which at present have provided the large majority of NEO diameters and albedos (Delbò, 2004). The limiting magnitude for obtaining good-quality thermal infrared data of NEOs is V ∼ 16.5 for a 4 m class telescope and V ∼ 18 for a 10 m class telescope, such as the Keck (Delbò, 2004; Delbò and Harris, 2002). This makes it impractical, if not impossible, to obtain data on asteroids as small as Apophis in the thermal infrared using ground based facilities. Large space-based infrared telescopes, such as Spitzer, have the required sensitivity to observe the weak thermal infrared flux from V > 18 asteroids. Note that Spitzer’s most sensitive band for detecting asteroids at heliocentric distances of ∼1 AU is at 8 µm. The thermal emission from asteroids at this distance peak near 10 µm and Spitzer can observe main-belt asteroids (whose thermal emission peaks in the 10–15 µm region) with V mags fainter than 21 (Tedesco et al., in preparation).

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However, space-based infrared instruments have stringent pointing constraints, e.g., Apophis is not in the Spitzer visibility region during the remainder of the mission. As of 17 May 2006, the NASA JPL impact risk web page (http://neo.jpl. nasa.gov/risk/) listed 105 potential Earth impactors. From this list we removed objects which were not classified as NEOs in the database of the Minor Planet Center (very likely lost) and asteroids with H > 24 (corresponding to asteroids with diameters <150 m for the lowest observed albedo, 0.02) to produce a list containing 31 NEOs. We estimated, for the next ten years, the number of these that can be observed in the thermal infrared compared to those for which we can obtain polarimetric data. We assumed that the observational constraints for ground based thermal infrared observations at a 10 m class telescope are: V  18, a solar elongation 50◦ , and an observing window 15 days. The observational constraints assumed for polarimetric observations at a VLT class telescope are: V  22, a solar elongation 50◦ , a phase angle 80◦ and 15◦ and an observing window 15 days during which the phase angle varies by 15◦ (the last constraints are to measure the slope of the polarization-phase curve). We found 4 NEOs observable in the thermal infrared using the 10 m Keck telescope vs 17 for which polarimetric data can be obtained using the 8.2 m VLT. Thus, VLT polarimetry can obtain reliable albedos and sizes, as demonstrated by the results for Apophis presented here, for at least four times as many hazardous NEOs, as could be observed in the thermal infrared from the ground using the Keck and in reasonable amounts of observing time (i.e., a total of 8-h at the VLT for V = 22). 5. Conclusions From polarimetric and photometric observations obtained with FORS1 at the VLT we have derived a visual geometric albedo of 0.33 ± 0.08 and diameter of 270 ± 60 m for the asteroid 99942 Apophis. The results presented here demonstrate that the VLT/FORS1 used in polarimetric mode is well suited to deriving albedos of NEOs with diameters on the order of a few hundred meters. Over the next decade this instrument is capable of obtaining reliable albedos and diameters for about 55% of the 31 known PHAs, and even more if they are observed during their discovery apparitions. For purposes of NEO albedo determination, polarimetry is clearly the most promising technique available now and for the foreseeable future. Acknowledgments We thank the staff and the Science Archive Operation of the European Southern Observatory (ESO), in particular Marina Rejkuba, for their support to our observations. The work of M. Delbò was supported by the European Space Agency (ESA) and that of E. Tedesco by the National Aeronautics and Space Administration (NASA) under Grant NNG04GK46G, issued through the Office of Space Science Research and Analysis Programs. We thank the two referees, A.W. Harris (USA) and S. Chesley, whose useful and constructive reviews led to a significant improvement of this paper. References Appenzeller, I., and 18 colleagues, 1998. Successful commissioning of FORS1—The first optical instrument on the VLT. The Messenger 94, 1–6.

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